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Adiabatic quantum state generation and statistical zero knowledge
TLDR
The ASG approach to quantum algorithms provides intriguing links between quantum computation and many different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, statistical zero knowledge, and quantum random walks.
Quantum walks on graphs
TLDR
A lower bound on the possible speed up by quantum walks for general graphs is given, showing that quantum walks can be at most polynomially faster than their classical counterparts.
Fault-tolerant quantum computation with constant error
TLDR
This paper shows how to perform fault tolerant quantum computation when the error probability, q, is smaller than some constant threshold, q.. the cost is polylogarithmic in time and space, and no measurements are used during the quantum computation.
Quantum circuits with mixed states
TLDR
A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.
Adiabatic quantum computation is equivalent to standard quantum computation
TLDR
The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown, so this result implies that the adiABatic computation model and the standard quantum circuit model are polynomially equivalent.
Fault-Tolerant Quantum Computation with Constant Error Rate
TLDR
This paper provides a self-contained and complete proof of universal fault-tolerant quantum computation in the presence of local noise, and shows that local noise is in principle not an obstacle for scalable quantum computation.
Interactive Proofs For Quantum Computations
TLDR
Any language in BQP has a QPIP, and moreover, a fault tolerant one, and two proofs are provided: the simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements, which is not fault tolerant.
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial
TLDR
An explicit and simplePolynomial quantum algorithm to approximate the Jones polynomial of an n strands braid with m crossings at any primitive root of unity e2πi/k, where the running time of the algorithm is polynometric in m, n and k.
The Power of Quantum Systems on a Line
TLDR
The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Some illegal configurations cannot be ruled out by local checks, and are instead ruled out because they would, in the future, evolve into a state which can be seen locally to be illegal.
Lattice problems in NP ∩ coNP
We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of &nradic; lie in NP intersect coNP. The result (almost) subsumes the three
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